Lockhart-Martinelli correlation parameters

Thus, both flows are turbulent and the Lockhart-Martinelli correlation parameters for Re > 5 X lO from Table 7.14 are the appropriate ones to use, namely, m = n —0.2 and C = C(- = 0.184. The two-phase flow parameter X in Eq. (7.77) for turbulent-turbulent flow after substitution of the correlation parameter reduces to... 

Zhao and Bi (2001b) measured pressure drop in triangular conventional size channels d = 0.866—2.866 mm). The variations of the measured two-phase frictional multiplier with the Martinelli parameter X for the three miniature triangular channels used in experiments are displayed, respectively, in Fig. 5.29a-c. In Fig. 5.29 also shown are the curves predicted by Eq. (5.25) for C = 5 and C = 20. It is evident from Fig. 5.29 that the experimental data are reasonably predicted by the Lockhart-Martinelli correlation, reflected by the fact that all the data largely fall between the curves for C = 5 and C = 20, except for the case at very low superficial liquid velocities. 

The Lockhart-Martinelli correlation provides the relationship between 4>j. and the Martinelli parameter X . Therefore, use of equation 7.95 enables the relationship between 4>lo and X at low pressures to be found. 

Lazarek and Black [67] obtained good predictions of their data by using a value of 30 in the generalized Chisholm/Lockhart-Martinelli correlation for C. Mishima and Hibiki [66] obtained reasonably good predictions for their frictional pressure drop data for air-water flows by correlating the Chrisholm C parameter in the Lockhart-Martinelli correlation as a function of the tube diameter as follows ... 

For our purposes, a rough estimate for general two-phase situations can be achieved with the Lockhart and Martinelli correlation. Perry s has a writeup on this correlation. To apply the method, each phase s pressure drop is calculated as though it alone was in the line. Then the following parameter is calculated ... 

The Lockhart and Martinelli (1949) correlation also uses a two-phase friction multiplier, defined by Eq. (5.16). The friction multiplier has been correlated in terms of the Lockhart-Martinelli parameter, X, given by... 

Figure 5.31 shows a comparison of the two-phase friction multiplier data with the values predicted by Eq. (5.25) with C = 5, for both phases being laminar, and with C = 0.66 given by Mishima and Hibiki s (1996) correlation. It is clear that the data correlate well using a Lockhart-Martinelli parameter, but the predictions of... 

Martinelli and Nelson (M7) developed a procedure for calculating the pressure drop in tubular systems with forced-circulation boiling. The procedure, which includes the accelerative effects due to phase change while assuming each phase is an incompressible fluid, is an extrapolation of the Lockhart and Martinelli x parameter correlation. Other pressure drop calculation procedures have been proposed for forced-circulation phase-change systems however, these suffer severe shortcomings, and have not proved more accurate than the Martinelli and Nelson method. 

Hughmark and Pressburg (H12) have correlated statistically their void data and others for vertical flow, using a modified Lockhart-Martinelli parameter, X, given as... 

Again referring to Fig. 13, the same general trend is apparent in both the pressure-drop and number-of-transfer-unit curves. This suggests that another empirical correlating procedure could be arrived at for example, an approximate relationship exists between the length of a transfer unit (LTU) and the Lockhart-Martinelli parameters, X. 

Concurrent flow of liquid and gas can be simulated by the homogeneous model of Section 6.8.1 and Eqs. 6.109 or 6.112, but several adequate correlations of separated flows in terms of Lockhart-Martinelli parameters of pipeline flow type are available. A number of them is cited by Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, New York, 1979, p. 184). The correlation of Sato (1973) is shown on Figure 6.9 and is represented by either... 

A method for predicting pressure drop and volume fraction for non-Newtonian fluids in annular flow has been proposed by Eisen-berg and Weinberger (AlChE J., 25, 240-245 [1979]). Das, Biswas, and Matra (Can. J. Chem. Eng., 70, 431—437 [1993]) studied holdup in both horizontal and vertical gas/liquid flow with non-Newtonian liquids. Farooqi and Richardson Trans. Inst. Chem. Engrs., 60, 292-305, 323-333 [1982]) developed correlations for holdup and pressure drop for gas/non-Newtonian liquid horizontal flow. They used a modified Lockhart-Martinelli parameter for non-Newtonian... 

Basically, two types of correlation for the dynamic or total liquid holdup are reported in the literature. Some investigators have correlated the liquid holdup directly to the liquid velocity nd fluid properties by either dimensional or dimensionless relations. In more recent investigations, the liquid holdup is correlated to the Lockhart-Martinelli parameter APl/APg (or an equivalent of it. as discussed in the earlier section). 

Sato et al.27 correlated liquid holdup to the Lockhart-Martinelli parameter for the pressure drop. Based on their own data, they obtained a relation... 

This can be readily integrated numerically as long as we use the appropriate nonequilibrium equivalent specific volume v, in the integration. A reasonably simple form for o, has been suggested by Chisholm (1983), which makes use of established correlations for the slip velocity K, which depends on the Lockhart-Martinelli parameter X Integrating Eq. (26-118) gives ... 

The existing hydrodynamic models can be broadly classified into two different categories on the basis of empirical approach and theoretical approach. The empirical approach is based on dimensional analysis to produce explicit correlations for pressure drop and liquid holdup using flow variables and packing characteristics or using the Lockhart-Martinelli parameter, which was proposed for open horizontal The theoretical... 

The pressure drop for concurrent downflow of gas and liquid in a packed bed can be predicted using correlations of the Lockhart-Martinelli type [22]. The pressure drop for each phase flowing separately through the bed is calculated using the Ergun equation [Eq. (3.64)], and these values define a parameter x ... 

The two equations given above are correlated in terms of a dimensionless number called the Lockhart-Martinelli parameter (. It is the ratio of the singlephase pressure drop of liquid to that of the gas and given by... 

When both phases are in turbulent flow, or when one phase is discontinuous as in bubble flow, it is not presently possible to formulate the proper boundary conditions and to solve the equations of motion. Therefore, numerous experimental studies have been conducted where the holdups and/or the pressure drop were measured and then correlated as a function of the operating conditions and system parameters. One of the most widely used correlations is that of Lockhart and Martinelli (L12), who assumed that the pressure drop in each phase could be calculated from the equations... 

Lockhart and Martinelli divided gas-liquid flows into four cases (1) laminar gas-laminar liquid (2) turbulent gas-laminar liquid (3) laminar gas-turbulent liquid and (4) turbulent gas-turbulent liquid. They measured two-phase pressure drops and correlated the value of 0g with parameter % for each case. The authors presented a plot of acceleration effects, incompressible flow (3) no interaction at the interface and (4) the pressure drop in the gas phase equals the pressure drop in the liquid phase. 

Dengler and Addoms 8 measured heat transfer to water boiling in a 6 m tube and found that the heat flux increased steadily up the tube as the percentage of vapour increased, as shown in Figure 14.4. Where convection was predominant, the data were correlated using the ratio of the observed two-phase heat transfer coefficient (htp) to that which would be obtained had the same total mass flow been all liquid (hi) as the ordinate. As discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt, the parameter for two-phase turbulent flow developed by Lockhart and Martinelli(9). The liquid coefficient hL is given by ... 

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